is this just a polynomial thing?
#help-49
drifting root
fossil knot
hm I'm not actually sure if this works though
fossil knot
like 6 and 8, 2 is a factor so its true for 14
yes
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last slate
There are 50 identically-shaped marbles in a bag: 17 red, 17 blue, and 16 green. Bill is randomly pulling out marbles one-by-one without replacement.
midnight plankBOT
There are 50 identically-shaped marbles in a bag: 17 red, 17 blue, and 16 green....
last slate
Is the probability that a red marble is pulled out third the same as the probability that a red marble is pulled out tenth?
My answer: yes because each arrangement has uniform probability distribution, so swapping third and tenth marble is a bijection and hence has the same cardinality
last slate
hi slayyy layla 💅
dawn dagger
I first understood it wrong but I think I agree
last slate
the answer they gave me was “we can’t say much about their cardinality without additional information”
last slate
I first understood it wrong but I think I agree
junior flower
the answer they gave me was “we can’t say much about their cardinality without a...
lol they are definitely the same
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last slate
lol they are definitely the same
alright thanks, i’ll believe me and you over my prof
junior flower
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wind oxide
is $\prod_{i=a}^{b} f(i) = \prod_{i=g(a)}^{g(b)} g^{-1}(f(i))$?
midnight plankBOT
is $\prod_{i=a}^{b} f(i) = \prod_{i=g(a)}^{g(b)} g^{-1}(f(i))$?
grand pondBOT
rak³en
wind oxide
under the assumption that $f : \mathbb{N} \to \mathbb{N}$ is a bijective function, same for $g$. They are both continious on the non-negative integers
wind oxide
**rak³en**
Quite sure this isn't true for most functions; I am here to ask what necessary conditions need to be established for this equality to hold true
junior flower
not for an arbitrary bijection g
wind oxide
not for an arbitrary bijection g
well thats what i said - for any arbitary functions f and g this probably isnt true. I am here to ask what properties f and g need to have for this to be true
wind oxide
and multiply the productand by k
also does this example work? i have no idea
wait it doesnt
junior flower
well i'm telling you bijective is not enough
and like
this doesn't look very nice
i wouldn't expect any nice conditions to be sufficient
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dawn dagger
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red cave
how do i solve this
red cave
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last slate
**rak³en**
I've been waiting for this moment... for the past year...#help-5 message @wind oxide
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reef pendant
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reef pendant
where do I even start?
noble mural
p > 100; p = -2q^2 + 34q + 40
-> -2q^2 + 34q + 40 > 100
-> -2q^2 + 34q - 60 > 0
factorize and im sure u know what to do after that
reef pendant
the concept of the question is diabolical
noble mural
p > 100; p = -2q^2 + 34q + 40
starting from here there has been no mistake right ? it is just right from the text
im just interpreting it
to get the bounds of "q"
reef pendant
lemme take time to factorize
noble mural
ok -)
reef pendant
−2q²+34q−60=−2(q−15)(q−2), I feel like I'm not on the right track.
noble mural
−2q²+34q−60=−2(q−15)(q−2), I feel like I'm not on the right track.
ur on the perfect track 💀
chill
u sure that ur factirizing is correct ye ? im too lazy to do this
noble mural
−2q²+34q−60=−2(q−15)(q−2), I feel like I'm not on the right track.
anyway this sounds right
noble mural
-> -2q^2 + 34q - 60 > 0
-> -2(q-15)(q-2) > 0
=> (q-15)(q-2) < 0
assess the situations
warped horizon
the concept of the question is diabolical
reef pendant
2 < q< 15
reef pendant
this Singapore math challenge is quite challenging, anyways thanks
reef pendant
.close
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twilit field
Can I have this verified
midnight plankBOT
Can I have this verified
warped horizon
yeah but when you sub in min of x assuming x > 1, you drop the equal to part of the less than or equal to
visual tiger
well you didn't prove what was asked first of all
and then this justification is vague at best
it could be better just proving that (5-3x)/2 < 1
and then y <= something < 1
twilit field
OK,thanks
junior flower
you seem to be using the fact that over [1,infty), this is maximized when x = 1
but like you should explain that
twilit field
junior flower
and would also need to tighten the <= after that
twilit field
Like this?
junior flower
why >= ?
warped horizon
x > 1
3x > 3
-3x < -3
5 - 3x < 2
(5 - 3x)/2 < 1
warped horizon
make sure you flip the inequality sign when you subtract 3x
your second and third lines aren't equivalent
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hollow oyster
hmm ok
hollow oyster
i have a question
how to prove that $\lim_{x \to 0}\frac{\log(1+x)}{x}=1$ without using Lhospital rule or power series?
grand pondBOT
convergence
hollow oyster
rewrite the limit again
?
surreal moon
how to prove that $\lim_{x \to 0}\frac{\log(1+x)}{x}=1$ without using Lhospital ...
Consider the definition of e
gaunt nimbus
then make substitution
surreal moon
slide me help
!occupied
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minor isle
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minor isle
How do I factorize this polynomial
last slate
you can first find out one of its root just by hit and trial method
minor isle
so just guessing?
minor isle
alright
last slate
we usually check 1,-1,2,-2
minor isle
oh yeah 1 is a root
checks out
is there a different method?
like a method which works 100% of the time
minor isle
alright
minor isle
now we divide the polynomial with x-1
which gives us a quadratic which we can factorize?
last slate
np
minor isle
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fallen aurora
(Multiple correct choice{s})
Is there any efficient way than to just verify each option separately?
midnight plankBOT
(Multiple correct choice{s})
Is there any efficient way than to just verify each...
@fallen aurora Has your question been resolved?
fallen aurora
<@&286206848099549185>
visual tiger
geometric sum
fallen aurora
geometric sum
That's not my problem
visual tiger
I would just try to simplify xyz
fallen aurora
I would just try to simplify xyz
I have tried so much but it's just keeps getting worse
visual tiger
like x = cosec(x)^2, y = sec(x)^2 and z = 1/(1-sin(2x)^2/4))
so computing xyz shouldn't be that bad
then again computing xz+y, xy+z, etc
is not a big deal either
fallen aurora
so computing xyz shouldn't be that bad
I mean like they aren't getting simplified
feral sedge
like x = cosec(x)^2, y = sec(x)^2 and z = 1/(1-sin(2x)^2/4))
(this isn't z)
feral sedge
i think 2 should be 4
visual tiger
ok
fallen aurora
ig
i have to verify all the options, that's the only method right?
nm
thanks for the help
.close
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wide marsh
hi guys i have a quick question about determining the radius of convergence of a power series
midnight plankBOT
hi guys i have a quick question about determining the radius of convergence of a...
wide marsh
so when you do the ratio test to find limit L of the series an when n goes to infinity:
If L=0, the radius of convergence is infinite, ie. X can be all real numbers
If L=inf, the radius of convergence is 0, ie. X can only be the center of convergence
can anyone confirm this
junior flower
the value of the limit should depend on x what is
wide marsh
huh wdym
when you use ratio test to determine convergence?
doesnt ratio test just give you a limit L when n goes to infinity and for a series to converge L must be less than 1
wild cloak
wide marsh
yes thats what im talking about
junior flower
do you have an example we can look at
wide marsh
dont you just make an inequality of L<1
this is correct right
i forgot to write the lim n-> inf in all lines but yeah
junior flower
oh, ok, sure, if the limit is 0 for all x, then yes the series converges for all x
wide marsh
ok so what if the limit is inf
does it converge for one value of x and diverge the rest of always diverging
junior flower
a power series always converges at its center
junior flower
but yea it diverges everywhere else in that case
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spare marlin
So first a bit of context.
I'm working on understanding how to implement Barrett Reduction for performing modular reduction on large binary unsigned integers.
From my understanding of the algorithm, Barrett reduction essentially attempts to compute the quotient of the number being reduced with the modulus, then subtracts the product of the quotient and the modulus to extract a remainder which is the output.
This looks like:
quotient = floor(div(a, modulus))
product = quotient * modulus
remainder = a - product
return(remainder)
However, computing the division can be expensive if you need to perform the modular reduction for a fixed modulus often. Barret reduction solves this problem by approximating this by computing the following relationship:
floor((1/modulus) * a) = quotient
floor(((2^k)/modulus) * a) / (2^k)) = quotient
approximate_fraction = floor((2^k)/m) (This is the part that gets precomputed and reused across multiple modular reductions)
floor((approximate_fraction * a) / (2^k)) = approximate_quotient
This allows us to implement the reduction like so:
def barrett_reduction_core(a, modulus, k):
# The computation of the fraction can be cached for modular reduction using the same modulus
fraction = floor((2^k) / modulus)
fraction_product = a * fraction
approximate_quotient = floor(fraction_product / (2^k))
approximate_product = approximate_quotient * modulus
approximate_remainder = a - approximate_product
# A couple additional loops are included to ensure the actual remainder is in the appropiate range since the approximate remainder may be larger than the valid interval.
Notably, the approximate quotient will have an error that is related to the lost fractional part of (2^k)/m. This error is multiplied by a.
Now, here's the question.
Given a modulus m in the range of 2^(x-1) to (2^x)-1 where x is a positive integer (ie m is x bits wide)
And using a = (2^y)-1 (ie a is the max possible unsigned integer for y bits)
What is the smallest possible value for k(positive integer) such that:
( a * ((2^k)/m)) - ( a * floor(((2^k)/m)) <= b
where b is a small positive integer(for the simple case, assume b == 1)
If I can get a solution for the smallest valid value of k given x and y, this would be extremely helpful.
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@spare marlin Has your question been resolved?
spare marlin
<@&286206848099549185>
midnight plankBOT
@spare marlin Has your question been resolved?
spare marlin
Second time check
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@spare marlin Has your question been resolved?
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@spare marlin Has your question been resolved?
wind oxide
@spare marlin you might want to ask in the comp sci server, maybe someone there knows about barrett reduction
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@spare marlin Has your question been resolved?
spare marlin
<@711177946135789588> you might want to ask in the comp sci server, maybe someon...
Do you have a link?
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fallen aurora
Could someone explain, how the diagram will be drawn for this question?
midnight plankBOT
Could someone explain, how the diagram will be drawn for this question?
fallen aurora
The diagram they made in the solution is making no sense to me
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fallen aurora
<@&286206848099549185>
delicate helm
i'm pretty sure "perpendicular" is supposed to be the height (aka altitude) from the right angle to the hypotenuse
fallen aurora
i'm pretty sure "perpendicular" is supposed to be the height (aka altitude) from...
yup I got that
see, that's the problem
I don't get how they made this diagram
gusty birch
I think this should be the diagram that explains the situation
you can show that alpha = 180deg-90deg-gamma, so alpha = 90deg-gamma (written as theta in the diagram); although i think its more useful to write it as pi/2 rad - gamma
fallen aurora
why can't we just draw a simple right triangle?
or is it just the language of the question, that I don't understand?
gusty birch
why can't we just draw a simple right triangle?
wdym by a simple right triangle?
fallen aurora
like just one triangle without partition
gusty birch
the question asks you to partition the triangle into 2 so i dont think that can be avoided
fallen aurora
the question asks you to partition the triangle into 2 so i dont think that can ...
okay, so it is just that I didn't understood question correctly
gusty birch
tbh i dont really understand it either haha, by "other acute angles" does it mean alpha and gamma or the ones formed by the line X and the right angle?
fallen aurora
tbh i dont really understand it either haha, by "other acute angles" does it mea...
that's what I am confused about too
In the solution they just have this diagram and calculation that has nothing to do with the diagram
gusty birch
i would just look for both and see which one of the 2 pairs are options and which isnt
i would assume by their diagram that they are asking you to find alpha and gamma, since the other 2 arent noted
fallen aurora
i would assume by their diagram that they are asking you to find alpha and gamma...
yeah OKOK
tysm
gusty birch
yw :)
delicate helm
tbh i dont really understand it either haha, by "other acute angles" does it mea...
they are equal, actually
fallen aurora
they are equal, actually
how?
delicate helm
by similarity of triangles, or by sum of the angles = 180°
fallen aurora
if they are equal then the answer would be C which is clearly not the case
gusty birch
altho alpha and gamma could be equal, you need to do the calculations to find that out
nvm i just understood what you meant
yea you can prove that the red angle is equal to gamma and the blue angle is equal to alpha by similarity of triangles pretty easily
fallen aurora
yea you can prove that the red angle is equal to gamma and the blue angle is equ...
okay ig
then I will try it out
thank for the help Mr. woomy and and Mr. CyclicTree
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gusty birch
yw! :)
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twilit coyote
How to do this
midnight plankBOT
How to do this
twilit coyote
a is an integer strictly greater than 1 btw
fallen aurora
How to do this
what do you want to find?
twilit coyote
what do you want to find?
set of solutions (x ; y) from Z×Z
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twilit coyote
<@&286206848099549185>
twilit coyote
Are you familiar with Bézout's lemma
no
pearl idol
OK it says that ax + by = 1 has solutions if and only if a and b are coprime
And if they are coprime, you can find solutions using the Euclidean algorithm
twilit coyote
So i have to prove that a² + a - 2 and -a - 2 are coprime?
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blissful drum
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blissful drum
i need help with understanding their work process
astral garnet
is it the stuff in the purple?
astral garnet
right so the velocity change from A to B is just the difference in their velocity vectors i.e v_b - v_a (final - initial) which is essentially just a line staring from the tip of v_a to the tip of v_b, you can see this by turn v_b - v_a into v_b + (-v_a) and just adding the 2 vectors and finding the resultant. Similarly we can apply those same things to B and C
midnight plankBOT
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stable mirage
why would it be .6?
midnight plankBOT
why would it be .6?
stable mirage
$dy/dx = e^x$
grand pondBOT
MWB117
stable mirage
$dy = e^x * .6$
grand pondBOT
MWB117
stable mirage
and wouldnt x be .6?
vernal patio
What is the question?
midnight plankBOT
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candid charm
Can someone help me with this, im stuck on why the answer is squared at the end
candid charm
thats the answer^
i got it up to here, im missing the ^2 on the outside
i made u=cos2x
du = -2sin2x dx
du/-2 = sin2x dx
plugged that back into the equation
ended up with -1/2 ∫u*du
-1/4(sin2x) + C
is what i end up with
let me know where im messing up
olive matrix
candid charm
u = cos2x?
midnight plankBOT
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@candid charm Has your question been resolved?
oak glade
Can someone help me with this, im stuck on why the answer is squared at the end
Demoivres theorem
Oh wait
oak glade
Can someone help me with this, im stuck on why the answer is squared at the end
You can use sub
💀💀
candid charm
i still dont get it with u sub
candid charm
-1/2 ∫u du = -1/4 u^2 + c
why is it ^2?
like i have done questions where it was sin^2x so for that i used u^2, but this is sin2x?
hybrid crane
No problem!
minor isle
midnight plankBOT
minor isle
ive tried using the general formula for geometric sequence to find a value for n that works in this
but i cant take the log of a negative number
last slate
What’d you get as the nth term for the sequence ?
minor isle
minor isle
What’d you get as the nth term for the sequence ?
thats the problem
i cant get an nth term for this one
minor isle
yeah the common ratio is -4 right?
shy ice
So since you found the ratio you can just divide 49152 by -4 until it gets to 3 it tbh
last slate
Then show that 16375 isn’t divisible by 4
shy ice
Mm
minor isle
i see
but isnt there a way which i can utilize the formula
this is just trying every possibility kind of
shy ice
49152/3 = 16375?
last slate
but isnt there a way which i can utilize the formula
using the formula
And then getting (-4)^n-1
minor isle
49152/3 = 16375?
sorry my mistake its 16384
shy ice
Yes correct
last slate
Oh I didn’t check that 😭
shy ice
Now you just have to prove 4^ of something = 16384 or not
shy ice
Well 4^ even number
minor isle
alright i see
shy ice
Yea try it out
minor isle
yeah so im getting 4^7 = 16384
but its odd
so its not in the sequence?
conclusion:
-49152 is in the sequence however 49152 is not
is this correct?
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dense viper
I'm trying to solve for x where x is the smallest possible real number:
⌊x^2⌋−x⌊x⌋=6
I'm starting with n = ⌊x⌋ and r = x - ⌊x⌋ (meaning 0 <= r < 1) or x = r + n as substitutions.
This takes the original equation to
⌊(n+r)^2⌋ - (r + n)*n = 6
I expand and simplify this out to
⌊n^2 + 2nr + r^2⌋ - n^2 - nr = 6 .
However I'm not sure where to proceed from here.
I know that n^2 <= (n+r)^2 < (n+1)^2
but if I substitute (n^2) for (n+r)^2, I get
n^2 - n^2 - nr = 6
nr = -6
r = -6/n
and then plug back to the substitution
0 <= r < 1
0 <= -6/n < 1
0 <= -6 < n
This seems like it implies I made a mistake.
midnight plankBOT
I'm trying to solve for x where x is the smallest possible real number:
> ⌊x^2⌋...
hollow iron
I'm trying to solve for x where x is the smallest possible real number:
> ⌊x^2⌋...
given the expanded equation
see that the floor of n^2+something is just n^2+the floor of that something
because n^2 is integer
this cancels out the n^2
dense viper
ah so like
⌊n^2 + 2nr + r^2⌋ - n^2 - nr = 6
⌊2nr + r^2⌋ - nr = 6?
hollow iron
ah so like
> ⌊n^2 + 2nr + r^2⌋ - n^2 - nr = 6
> ⌊2nr + r^2⌋ - nr = 6?
yeah
thats right
but now you see that nr is integer
it just beomes nr=6 after simplifying using the fact nr is integer
dense viper
Is it really safe to say that nr is an integer? I thought since 0 <= r < 1, that would imply that nr is potentially not an integer.
hollow iron
Is it really safe to say that nr is an integer? I thought since 0 <= r < 1, that...
yes it is safe
notice that 6- the floor is an integer
thus nr is an integer
dense viper
Ah!! So then because 2nr is an integer, we can pull it out of the floor and since floor of r = 0, it'll simplify down to
2nr - nr = 6
nr = 6..
And then I can proceed to plug that back into the inequality of r
hollow iron
Ah!! So then because 2nr is an integer, we can pull it out of the floor and sinc...
exactly
so that means n>=7
dense viper
perfect, thank you
that solved my road block and I can sleep in peace haha
hollow iron
perfect, thank you
that solved my road block and I can sleep in peace haha
have a good sleep
opaque flame
A field is it should be commutative on both operations?
midnight plankBOT
A field is it should be commutative on both operations?
@opaque flame Has your question been resolved?
rose trout
Yes
robust shale
what does it mean by formula for T inverse?
midnight plankBOT
what does it mean by formula for T inverse?
robust shale
I got
$det(T) = -6$
and
$A^{-1} =
\begin {bmatrix}
\frac{-7}{6}& \frac{-8}{6}\
-1 & -1
\end{bmatrix}$
grand pondBOT
unbearablefrequentist1
robust shale
Linear Algebra Question
rose trout
Just like they have given you T(x1, x2) in a formula at the start, they want you to translate your inverse matrix back into a formula
midnight plankBOT
@robust shale Has your question been resolved?
robust shale
Just like they have given you T(x1, x2) in a formula at the start, they want you...
does that mean write this?
but for the inverse
rose trout
Yes
grand pondBOT
unbearablefrequentist1
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blissful drum
midnight plankBOT
blissful drum
i dont get why this isnt after marker 1
his explanation was that since at the beginning, it takes longer to accelerate or that it will travel less distance during that period
so when it reaches the half way point, wouldnt it be after marker 1 as it took longer to reach
<@&286206848099549185>
earnest bluff
it's a
earnest bluff
i dont get why this isnt after marker 1
are you familiar with newton's laws of motions
or galileo
midnight plankBOT
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cobalt dragon
i had a question. want to see if my answer is right.
1 card drawn from pack of 52 playing cards. what is probability that it is red or a king.
my answer is 4/52+26/52-2.
is this right
midnight plankBOT
i had a question. want to see if my answer is right.
1 card drawn from pack of ...
slender walrus
as written, no
slender walrus
why's the -2 on the very end
slender walrus
subtract at the appropriate place
because i'm reading
$$\frac{4}{52} + \frac{26}{52} - 2$$
which is less than 0, which doesn't make sense when talking about probability
grand pondBOT
ℝαμΩℕωⅤ
slender walrus
then yes, that would be alright
cobalt dragon
$$\frac{4+26-2}{52}$$
grand pondBOT
cali_owt
cobalt dragon
then yes, that would be alright
can you tell if my reasoning is right
suppose we separate 4 kings (2 red+2 black), and 26 red cards. that is not possible. so either you separate 2 black kings and 26 red cards. or you separate 4 kings (2 black+2 red) and 24 red cards. because they have 2 cards in common. and since we are drawing only 1 card, so we subtract 2 cases
@slender walrus
slender walrus
viewing it with separation is a bit convoluted, don't bother
P(red) + P(king) - P(red king)
from inclusing/exclusion principle
cobalt dragon
and what if we want to draw 2 cards? and probability or both being red or both being king?
slender walrus
P(2 red) + P(2 kings) - P(2 red kings)
slender walrus
- P(2 red kings)
cobalt dragon
what will be that 😭
slender walrus
calculate the probability the same way you did for the others
cobalt dragon
2/52?
maybe 2/52×1/51?
@slender walrus
is my way of solving right? I use this fraction method where numerator is wanted case divided by total case?
slender walrus
yeh
cobalt dragon
my teacher uses combination in it. so he'll write like 2C2/52C2
cobalt dragon
maybe 2/52×1/51?
is this right
cobalt dragon
my teacher uses combination in it. so he'll write like 2C2/52C2
i understand combination but I think what's need of using combination when I know simpler method? @slender walrus
cobalt dragon
my teacher uses combination in it. so he'll write like 2C2/52C2
this also gives 2/52×1/51
slender walrus
more convenient when choosing larger amounts
cobalt dragon
> \- P(2 red kings)
so we have to subtract number of cards which are both red and king
cobalt dragon
is this right
is this right
slender walrus
number of pairs of cards
you're dealing with two cards here, not one
(or probability, depending on how you're counting)
cobalt dragon
is this right
is this right @slender walrus @slender walrus
@slender walrus @slender walrus
@slender walrus
surreal moon
is this right <@220517274845577216> <@220517274845577216>
Do not spam pings like this
cobalt dragon
pls tell answer 😭
@slender walrus you are telling every other thing but other than what I'm asking. I ask how i do this, and you say you have to do this. ffs I know what to do. all I'm asking what i did is right or wrong. and you only keep telling me what i already said. fo
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surreal moon
pls tell answer 😭
!noans
midnight plankBOT
pls tell answer 😭
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
slender walrus
i already said yes earlier
cobalt dragon
!noans
not talking to you smarty guy. i only said tell me is my answer right
@surreal moon i know how rules work here smarty ess
slender walrus
!volunteers
midnight plankBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
slender walrus
this type of behaviour isn't cool so don't expect any further help from me
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blissful drum
how would you solve a i.?
midnight plankBOT
how would you solve a i.?
blissful drum
i tried drawng a tangent line at (0,0) and estimated in which i got 4.8ms^-1
but the answer is 6...
<@&286206848099549185>
leaden oracle
i tried drawng a tangent line at (0,0) and estimated in which i got 4.8ms^-1
Pretty strange. This should give the correct answer
Is this all of the information?
midnight plankBOT
@blissful drum Has your question been resolved?
blissful drum
in the presence of acceleration, would a linear displacement vs time graph be impossible?
midnight plankBOT
in the presence of acceleration, would a linear displacement vs time graph be im...
misty gorge
it would be impossible, if you have a linear displacement vs time graph then you can find the acceleration by taking the derivative twice (if you don’t know about derivatives then don’t worry about it too much, just to say that this is the way to find acceleration) and you’ll find that it’s 0
blissful drum
ah ok
so if a question say provides you with a velocity-time graph with acceleration and whatnot and asks you to draw a displacement-time graph, you would draw a parabola not a linear as according to you, linear graphs has no acceleratoin?
misty gorge
so if a question say provides you with a velocity-time graph with acceleration a...
yeah, assuming that what you mean by “velocity time graph with acceleration and whatnot” means a linear velocity-time graph with nonzero slope
then your displacement graph will be a parabola
blissful drum
yeah, assuming that what you mean by “velocity time graph with acceleration and ...
yes yes
what so what if the velocity-time graph is non-linear
misty gorge
the underlying reason why this is true needs calculus
misty gorge
what so what if the velocity-time graph is non-linear
then you’re going to have to use calculus
blissful drum
the underlying reason why this is true needs calculus
trye
misty gorge
then you’re going to have to use calculus
but if you’re given an initial position then you can take the integral of your velocity graph
blissful drum
i see... i know calculus but ive never done kinematics calculus yet
blissful drum
but if you’re given an initial position then you can take the integral of your v...
alr
thank you
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wind oxide
Is their a function that interpolates the 'mod' function?
midnight plankBOT
Is their a function that interpolates the 'mod' function?
wind oxide
Here mod function means a function that returns the remainder of a number (integer) divided by a constant
wind oxide
depends on what you mean by interpolate
Ah yes for example, cos(pi*x) interpolates (-1)^t
Oh and I should post exactly what I first ig
So that no one xy's me
Looking for a closed form of the following
(n >= 1, k = a_0/2)
humble torrent
So like a function which behaves like mod(1,2) = 1, mod(2,2) = 0, etc?
runic hamlet
what exactly are you hoping from such a thing. you can easily write 1 % 2 = 1 and stuff, but you dont want that for whatever reason. an actual closed form (if it exists) will look much more complicated
are you allowing floor? probably not, right?
wind oxide
what exactly are you hoping from such a thing. you can easily write 1 % 2 = 1 an...
I don't know what I am looking for. Just something that can be written using existing functions
runic hamlet
% is an "existing" function
wind oxide
are you allowing floor? probably not, right?
I would like to avoid that. But if nothing works, might as well go with it
wind oxide
% is an "existing" function
Err... something more concrete I suppose. Maybe analytic is the word I am looking for 
Also isn't % an operation rather?
runic hamlet
f(x)=x%2 then
you should probably be able to set up a linear system of equations by using functions like cos(pi/2 x), cos(pi x), cos(3pi/2 x), cos(2 pi x) as your basis
dreamy lichen
Ah yes for example, cos(pi*x) interpolates (-1)^t
if you want trig one, check this $0.5-\frac{\cos\left(\pi x\right)}{2}$
grand pondBOT
MæthIsAlwaysRight
dreamy lichen
**MæthIsAlwaysRight**
this one looks like this
wind oxide
if you want trig one, check this $0.5-\frac{\cos\left(\pi x\right)}{2}$
I already have something like that (used it for solving a simpler recurrence)
dreamy lichen
wait, so what else do you need?
wind oxide
you should probably be able to set up a linear system of equations by using func...
Hmmm...maybe this works
wind oxide
Looking for a closed form of the following
This
wind oxide
wait, so what else do you need?
It won't work for mod 4
I Amma cook
Thx for the suggestion denascite
humble torrent
Looking for a closed form of the following
This looks like the best way to write it
hard umbra
is that like
wind oxide
If anyone else has any ideas, please do post it here!
wind oxide
This looks like the best way to write it
Could be..not that I care
humble torrent
This does feel a xy thing again tho, like why bother finding an uglier way to write it?
hard umbra
,, a_k = \begin{dcases*} 2k + 1, & if $k \equiv 1 \bmod 4$, \
-2(k + 1), & if $k \equiv 2 \bmod 4$, \
-(2k + 1), & if $k \equiv 3 \bmod 4$, \
2k, & if $k \equiv 0 \bmod 4$.
\end{dcases*}
grand pondBOT
humble torrent
And if anything more troublesome to work with
wind oxide
This does feel a xy thing again tho, like why bother finding an uglier way to wr...
I am studying a specific type of sequences. I can't really ask for help with that, can I?
hard umbra
is this what you wrote?
hard umbra
then what is k
wind oxide
(n >= 1, k = a_0/2)
.
hard umbra
what is a_0?
wind oxide
A constant, obviously
hard umbra
well not obviously
wind oxide
And it is an integer
hard umbra
so theres no change in the values at all is what you're saying
wind oxide
well not obviously
I mentioned n>=1 so I thought that made it obvious that a_0 can only be defined as a constant
wind oxide
so theres no change in the values at all is what you're saying
What?
Its a repeating sequence
wind oxide
Yes
hard umbra
okay well its really easy to make a function thats 1 on one particular residue class and 0 everywhere else
,w Table[(1^n + i^n + (-1)^n + (-i)^n)/4, {n, 0, 8}]
grand pondBOT
runic hamlet
roots of unity filtering, right
hard umbra
yes
runic hamlet
so much nicer
hard umbra
silly way to just write it in terms of indicator functions
hard umbra
well you get an "analytic" expression for the indicator functions
midnight plankBOT
hard umbra
presumably the cosine version is just the real part
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Available help channel!
normal furnace
How do you do this question
midnight plankBOT
How do you do this question
normal furnace
yea coz of the lines going through the side indicating they are equal
since two of the triangles are right angled
i mean three
c should be 70 right
stray mist
Wait is it given 3 triangles are right angled? I don't see that
stray mist
Then you can't say it's 90
normal furnace
ye true
stray mist
You need to prove it
normal furnace
as u said c is the easiest angle to figure out
stray mist
Anyways in the 70° triangles other 2 angles are equal as the 2 sides are radius
normal furnace
but idk how to find b
stray mist
So u can find those and apply in triangles with c as angle and from there it should be easy to find b
normal furnace
oh yea
i get it
so basically what u are saying is that since the triangle with 70 degrees
has two sides that are the samne angle
stray mist
Yes
normal furnace
u minus 180 from 70
stray mist
Yes
normal furnace
and then half it to find one angle
that would be 55
so its 70 and 55 right>
?
stray mist
Yes
normal furnace
thanks so much i used every help i can such as AI or from other students
and the answer was in plain sight
thanks
stray mist
No worries
normal furnace
it doesnt specify which one is wrong
if one of them is wrong the whole answer will appear wrong
normal furnace
u said that to find b i would need to minus 70 from 180 and then half the answer to find the angle that would equate to b
stray mist
No
normal furnace
or was that for c
normal furnace
yea i cant seem to find a clear answer
dw ill probs clarify it with my math teacher
coz my math program has some mistakes in the questions
i think this might be one of them
stray mist
Ya that's Good choice I think they forgot to mention 90° there
normal furnace
thanks anyways for the help
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lunar acorn
midnight plankBOT
lunar acorn
Hey there, can someone point out my mistake here ?
I sent my working steps there
<@&286206848099549185>
fallen aurora
!15m
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@lunar acorn Has your question been resolved?
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@lunar acorn Has your question been resolved?
remote spade
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i find these only with this information.
midnight plankBOT
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i f...
@remote spade Has your question been resolved?
vernal patio
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i f...
You sure this is the only info given?
remote spade
Yes.
fallen aurora
You'll get a_1 ig
but I can't figure out how to get d
remote spade
How do i get a(1)?
fallen aurora
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i f...
expand by the formula of S_n for AP
and put n=1
but I am not sure how you'll get d
vernal patio
expand by the formula of S_n for AP
Howw??
grand pondBOT
77²
fallen aurora
for S_n
vernal patio
And what will this be equated to?
fallen aurora
S(n^2) ig
fallen aurora
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i f...
it is given here
I mean the value we get for a(1) kinda concerns me, but I don't see any flaw in method
fallen aurora
Then this will also be S(1)
oh yeah,
you're right
that's the problem
!original
midnight plankBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
remote spade
This arithmetic sequence seems to start at 0 but i got no other things i can find for yhe time being.
fallen aurora
Then this will also be S(1)
What's your opinion on this?
vernal patio
I'm not able to translate this 😭
fallen aurora
If 4 * s(n) = s(n^2) then find a(1) and d of the arithmetic sequence.
How do i f...
well problem is just that
fallen aurora
Umm I tried to use the other formula of Sn
other?
vernal patio
There a & l will be the same for that series
fallen aurora
oh
fallen aurora
And I got n=4
Getting any values for n makes no sense ig
vernal patio
But again after putting n=4 eqn is still in a & d
vernal patio
Getting any values for n makes no sense ig
Right
remote spade
I'm not able to translate this 😭
This is said to be "4s(n) = s(n^2) then find a(1) and d."
vernal patio
This arithmetic sequence seems to start at 0 but i got no other things i can fin...
What do you mean by seems to start at 0?
remote spade
I plugged the n = 1 and it told me a(1) = 0.
vernal patio
I plugged the n = 1 and it told me a(1) = 0.
Huhh? How?
fallen aurora
I plugged the n = 1 and it told me a(1) = 0.
bro just ignore that method for now
oh I get it now
that piece of crap literally fooled all of us for a moment
vernal patio
What??
remote spade
Which part...
fallen aurora
Which part...
I meant the whole question
it is supposed to be easy but we are just overthinking it
vernal patio
Tell us!! FAST!!
fallen aurora
expand by the formula of S_n for AP
see after this step you just have to put values of n, and get two equations in "a" and "d"
and then solve for them
vernal patio
How do you get 2 eqns?
fallen aurora
How do you get 2 eqns?
like first put n=2 and then say n=3
vernal patio
Aaahhh
remote spade
Oh, it's that simple.
fallen aurora
you guys know about Presh Talwalker?
vernal patio
Nope
fallen aurora
that Mind Your Decisions youtube channel
remote spade
MindYourDecisions?
vernal patio
that Mind Your Decisions youtube channel
Nope
remote spade
Yeah, i have seen few videos of him.
fallen aurora
MindYourDecisions?
okay nvm
vernal patio
What about him?
vernal patio
like first put n=2 and then say n=3
Did you solve this?
fallen aurora
Yeah, i have seen few videos of him.
His next Video title be like:- a Greek question that stumped Indians and Greeks
fallen aurora
His next Video title be like:- a Greek question that stumped Indians and Greeks
he always has these types of titles
fallen aurora
Did you solve this?
yeah
fallen aurora
What did you get?
I mean not completely solved it
just made equations
vernal patio
I'm getting a=0 d=0 😭 😂
vernal patio
I AM DONEEEE
remote spade
I don't think this is possible.
vernal patio
I mean I can't do this further
vernal patio
I don't think this is possible.
Ofc not
@remote spade Bruh check the whole page for any extra info 😭
remote spade
Someone just told me that there is no way 4s(n) = s(n^2) can be a quadratic equation.
fallen aurora
oh wait I think there's no solution
remote spade
<@805288401263525938> Bruh check the whole page for any extra info 😭
Nope. There is nothing else.
vernal patio
oh wait I think there's no solution
Huh?
remote spade
Someone just told me that there is no way 4s(n) = s(n^2) can be a quadratic equa...
The relationship 4s(n) = s(n^2) cannot exist within an arithmetic sequence perhaps.
fallen aurora
The relationship 4s(n) = s(n^2) cannot exist within an arithmetic sequence perha...
Well considering a and d equals zero
that works
I don't think there's any condition on AP like GP
In GP you can't have a_n=0 or r=0
but in AP I think it is fine
vernal patio
There has to be some ans acc to me
fallen aurora
There has to be some ans acc to me
0 is indeed an answer but not sure if there's more
vernal patio
@remote spade Do you have it's final ans or something?
remote spade
I guess the only solution can be a(1) = 0 and d = 0. That is the only condition that satisfies 4s(n) = s(n^2)
There is no final answers on AP, GP or any sequence related chapters.
fallen aurora
,w 4S(n)=S(n^2)
grand pondBOT
fallen aurora
wtf
vernal patio
That Sn is creepy
remote spade
What...
fallen aurora
just ignore it
remote spade
I think a(1) and d both being 0 is enough for me to move on.
vernal patio
@fallen aurora I tried to write Sn^2 in terms of Sn but I'm not able to get anything
vernal patio
I think a(1) and d both being 0 is enough for me to move on.
Probably ask your teacher
remote spade
When the time comes i will. This is just my attempt on self-studying during summer holiday.
fallen aurora
When the time comes i will. This is just my attempt on self-studying during summ...
good thing lad
vernal patio
When the time comes i will. This is just my attempt on self-studying during summ...
Oh alright!
remote spade
Yeah, thanks for the help and spending your time on my problem, guys.
vernal patio
No worries!
fallen aurora
Yeah, thanks for the help and spending your time on my problem, guys.
np
remote spade
I really appreciate it. I will be closing this help section right now.
Bye and have a good day or night.
.close
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cobalt dragon
hi, probability question. 2 dice are thrown.
there are 2 events, A & B.
A= sum of digits on both dice is 7
B= digit on first die is greater than second
im stuck in a concept before reaching solution.
sample space of A={ (1,6) (2,5) (3,4) (4,3) (5,2) (6,1)} 6 elements
P(A)=6/36
sample space of B={15 elements}
P(B)= 15/36
now to find A∩B, considering definition of A and B, there are only 3 cases in common= (4,3) (5,2) (6,1). where first digit is greater and sum is 7.
how to get probability of A∩B
midnight plankBOT
hi, probability question. 2 dice are thrown.
there are 2 events, A & B.
A= su...
zenith garden
is this correct?
midnight plankBOT
is this correct?
vernal patio
Yes
midnight plankBOT
midnight plankBOT
Available help channel!
snow vector
midnight plankBOT
snow vector
some help please
surreal moon
some help please
Looks like you just rewrite the line, but replace n with any positive number of your choice
surreal moon
Yeah that would be fine.
shell wigeon
Shouldn't x also be replaced?
surreal moon
Shouldn't x also be replaced?
That's not what the examples have done
snow vector
Yeah that would be fine.
can you help me on these 2
i dont udnerstand how
@surreal moon
surreal moon
can you help me on these 2
It's the exact same idea. Just copy the line but replace n with any negative number
snow vector
|x| >= -2 then x<= -3 or x>= -6
would this correct
surreal moon
|x| >= -2 then x<= -3 or x>= -6
Nah look how the example did it with |x|>-3
Do you know, in plain English, what |x|>-3 is saying?
toxic ravine
Modx
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slate sierra
midnight plankBOT
slate sierra
Question 4
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slate sierra
<@&286206848099549185>
midnight plankBOT
@slate sierra Has your question been resolved?
fathom knoll
Why dont u actually tell us what approach you've tried and where you're stuck rather than asking for a solution
midnight plankBOT
@slate sierra Has your question been resolved?
slate sierra
Why dont u actually tell us what approach you've tried and where you're stuck ra...
I don’t know how to approach the problem in the first place
last slate
right, so do the same for part b. substitute on both sides of the equation. rearange to get a similar form as part a, and solve for the initial conditions
slate sierra
right, so do the same for part b. substitute on both sides of the equation. rear...
On it
last slate
how's it going?
slate sierra
how's it going?
I completed Ty
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Available help channel!
last slate
I completed Ty
good job!
proud island
bruh
last slate
would u consider to close this channel, lol
idk how to, it wasnt my original question lol. someone elses
proud island
nah, your "good job!" made this channel, lol
proud island
idk how to, it wasnt my original question lol. someone elses
use .close
last slate
.close
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Available help channel!
acoustic sparrow
is there a way to solve 25-25e^(-2t)=20t?
midnight plankBOT
is there a way to solve 25-25e^(-2t)=20t?
severe cloud
Probably using something like the Lambert W function, or numerical methods like the Raphson-Newton method
acoustic sparrow
so only numerical methods?
severe cloud
I‘m not sure if Lambert W could be considered "algrebraic", so yeah I‘d assume so
Often times when you have exponentials and polynomials mixed you won‘t get nice answers
midnight plankBOT
severe cloud
It‘s also called product log if that can get your more info
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stiff viper
i'm uneducated, how do i put a center in (ABC)
midnight plankBOT
i'm uneducated, how do i put a center in (ABC)
midnight plankBOT
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last slate
hi, i have a question:
"i have a sample of 50 identical balls with different colors: 17 blue, 17 red, and 16 green"
A) Probability of pulling a red after drawing three times
B) probability of pulling a red after drawing 10 times
midnight plankBOT
hi, i have a question:
"i have a sample of 50 identical balls with different co...
last slate
The answer is that A = B but i'm having a bit of trouble formulating an argument
my explanation: if i define two sigma algebras such that they give you the event space of all 3-tuples and all 10-tuples, then the measure is preserved for some function f that maps the event space of the 3-tuple sigma algebra to the event space of the 10-tuple sigma algebra
ngl idk how to prove that claim, is there an easier way to think about this? Maybe in terms of bijections and such
midnight plankBOT
@last slate Has your question been resolved?
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@last slate Has your question been resolved?
midnight plankBOT
@last slate Has your question been resolved?
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@last slate Has your question been resolved?
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@last slate Has your question been resolved?
civic moth
hi, i have a question:
"i have a sample of 50 identical balls with different co...
Don't waste your time bro,no-one answers a probability question,
To solve this use multiplication theorem and baye's theorem
last slate
Don't waste your time bro,no-one answers a probability question,
To solve this u...
lol
also no, that takes insane computations. this is supposed to be non computational
dawn dagger
@subtle blaze
subtle blaze
Hi
I don’t think it’s that computationally hard
P(A) = P(draw 4 balls, fourth is red) that sounds like something that people know
Hmm if you draw 1 the probability is P(X₁ = 1) = 17/50
If you draw 2 the probability is P(X₂ = 1) = P(X₁ = 0, X₁ = 1) + P(X₁ = 1, X₂ = 1) = 33/50 * 17/49 + 17/50 * 16/49
,calc 33/50 * 17/49 + 17/50 * 16/49
grand pondBOT
Result:
0.34
,calc 17/50
grand pondBOT
Result:
0.34
Looks like my intuition is that it actually doesn’t matter how many you first draw
Perhaps proving that would be easier than showing specifically 4 and 11
@last slate
subtle blaze
If you draw 2 the probability is P(X₂ = 1) = P(X₁ = 0, X₁ = 1) + P(X₁ = 1, X₂ = ...
Here Xᵢ is a random variable that’s 1 if you draw a red on the ith draw, and 0 otherwise
midnight plankBOT
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junior flower
proof: it’s fucking obvious
permutations of the 50 balls (treating them all as distinguishable, so 50! permutations) with red in the 4th position and permutations of the 50 balls with red in the 11th position are in 1-1 correspondence, through the map that swaps 4 and 11
midnight plankBOT
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Available help channel!
craggy yew
how should i solve this?
midnight plankBOT
how should i solve this?
slow thorn
how should i solve this?
Try completing the right angled-triangles by pasting an identical one opposite to them to form a window-like shape as a whole; the answer should be a bit more obvious.
dense arch
you have the areas of all, so you can write the equation of the areas as how they are and then take the sides in common and name em x,y,z,w and you can find all then find the area of A
basically make a system of equations
craggy yew
you have the areas of all, so you can write the equation of the areas as how the...
i did try that but didnt succeed
slow thorn
i did try that but didnt succeed
The configuration must look something like this:
craggy yew
The configuration must look something like this:
yes im drawing it
slow thorn
Please note that the areas should be doubled.
craggy yew
The configuration must look something like this:
is that bottom left figure a square?
slow thorn
is that bottom left figure a square?
It need not necessarily be one.
Now, the only crucial step is to assume the common lengths and breadths as w, x, y, z, or as whatever you are comfortable with, as mentioned by @dense arch.
You should get four equations in terms of these variables.
Please report the equations you end up with if any problem arises.
craggy yew
Roger.
slow thorn
ok i think i got a bit too out of character
stuck gulch
uhm let me give you a better solution
label each side of the rectanlges w, x, y and z
find the areas of each shape in terms of w,x, y and z
then solve
.
stuck gulch
Now, the only crucial step is to assume the common lengths and breadths as w, x,...
oh did not read this mb.should have read the whole convo
stuck gulch
i don't know it either but that is what i got so wanted to confirm. send later the solution to confirm please
slow thorn
but wait, theres a better solution!
stuck gulch
enlighten me
slow thorn
The configuration must look something like this:
after getting this diagram, we can see that the ratio of the areas of the left rectangles is the same as the ratio of the areas of the right rectangles
2A:72 = 128:96
from this A can be easily found
stuck gulch
hmmm checks out
slow thorn
this is because the rectangles each have the same lengths and only breadths b1 and b2